Computation of the eigenvalues of a second-order boundary value problem with parameter dependent boundary conditions

KABATAŞ A., ŞENGÜL S.

AIMS Mathematics, vol.11, no.3, pp.6030-6049, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 11 Issue: 3
  • Publication Date: 2026
  • Doi Number: 10.3934/math.2026250
  • Journal Name: AIMS Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.6030-6049
  • Keywords: asymptotic approximation, boundary value problems, eigenvalues, interpolating element free Galerkin method
  • Karadeniz Technical University Affiliated: Yes

Abstract

Our purpose in this paper was to determine the eigenvalues of the boundary value problem with separated and parameter dependent boundary conditions when the potential function is integrable and symmetric. We first provided the asymptotic estimates of the eigenvalues of the related problem. Second, we computed numerical results for the eigenvalues using the interpolating element free Galerkin method. Then, a few examples are presented to illustrate the power of the method and compare the asymptotical and numerical results for consistency and validity.